The amplitude, frequency, and phase are fundamental measurements used to describe signals. Here's a brief explanation of each and their corresponding formulas:
Amplitude: The amplitude of a signal refers to the magnitude or strength of the signal. It measures the maximum displacement or intensity of the signal from its reference or equilibrium point.
Formula: A = max(|x(t)|), where A represents the amplitude and x(t) denotes the signal at a given time, t. The absolute value (| |) is taken to consider both positive and negative excursions.
Frequency: The frequency of a signal refers to the number of cycles or oscillations that occur in one unit of time. It measures how quickly the signal repeats itself.
Formula: f = 1 / T, where f represents the frequency and T denotes the period of the signal. The period (T) is the time taken for one complete cycle of the signal.
Alternatively, the frequency can also be expressed in terms of angular frequency (ω), which is the rate of change of phase with respect to time:
Formula: ω = 2πf, where ω represents the angular frequency and f is the frequency.
Phase: The phase of a signal indicates the position of the signal in its cycle at a given point in time. It measures the fraction of a complete cycle or the angular displacement of the signal from a reference point.
Formula: φ = 2πft + φ₀, where φ represents the phase, f is the frequency, t is the time, and φ₀ is the initial phase or phase offset.
The phase can also be expressed in terms of radians or degrees, depending on the convention used. It helps to determine the alignment or synchronization of multiple signals.
These measurements are crucial in various fields, such as signal processing, telecommunications, audio engineering, and many other areas where the analysis and manipulation of signals are involved.